The angles of a triangle are in the ratio 3:4:5. What is the measure of the smallest angle?

##45^@##

Let the smallest angle be ##3x##

The other two angles are ##4x## and ##5x##

The three angles add up to

##3x+4x+5x = 12x##

This should be equal to ##180^@##, hence

##12x=180^@ implies x = 180^@/12 = 15^@##

The smallest angle will thus be

##3x = 3 * 15^@ = 45^@##